PReLU: Yet Another Single-Layer Solution to the XOR Problem

This paper demonstrates that a single-layer neural network using Parametric Rectified Linear Unit (PReLU) activation can solve the XOR problem, a simple fact that has been overlooked so far. We compare this solution to the multi-layer perceptron (MLP) and the Growing Cosine Unit (GCU) activation function and explain why PReLU enables this capability. Our results show that the single-layer PReLU network can achieve 100% success rate in a wider range of learning rates while using only three learnable parameters.

https://arxiv.org/abs/2409.10821